A number of studies show that even with simple interaction protocols, swarms
of agents are able to converge to organized, coherent behaviors. Existing
literature on the subject provides a wide selection of both agent-based
[1]}, [2]}, [3]}, [4]} and continuum models
[5]}, [6]}, [7]}. One of the earliest
agent-based models of swarming is Reynolds's boids
[8]}, which simulates the motion of a group of flocking
birds. The boids follow three simple rules: collision avoidance, alignment
with neighbors, and attraction to neighbors. Since the publication of
Reynolds's paper, many models based on “zones” of attraction, repulsion,
and/or alignment have been used as a means of realistically modeling swarming
behaviors [9]}, [10]}, [11]}. Systematic numerical
studies of discrete flocking based on alignment with nearest neighbors we
carried out by Vicsek et al. [12]}. Stochastic
interactions between agents are modeled in [13]}. In recent years,
improved computer vision algorithms have allowed researchers to record and
analyze the motions of individual agents in biological flocks, and formulating
more accurate, empirical models for collective motion strategies of flocking
species including birds and fish [14]}, [15]}, [16]}.
